Problem: Jessica is 30 years older than Ishaan. Two years ago, Jessica was 4 times as old as Ishaan. How old is Ishaan now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Ishaan. Let Jessica's current age be $j$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $j = i + 30$ Two years ago, Jessica was $j - 2$ years old, and Ishaan was $i - 2$ years old. The information in the second sentence can be expressed in the following equation: $j - 2 = 4(i - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = i + 30$ . Substituting this into our second equation, we get the equation: $(i + 30)$ $-$ $2 = 4(i - 2)$ which combines the information about $i$ from both of our original equations. Simplifying both sides of this equation, we get: $i + 28 = 4 i - 8$ Solving for $i$ , we get: $3 i = 36$ $i = 12$.